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The tensile strength of silicone rubber is thought to be a function of curing temperature. A study was carried out in which samples of 12 specimens of the rubber were prepared using curing temperatures of 20 C and 45 C. The data below show the tensile strength values in megapascals. 20 C: 2.07 2.14 2.22 2.03 2.21 2.03 2.05 2.18 2.09 2.14 2.11 2.02 45"C: 2.52 2.15 2.49 2.03 2.37 2.05 1.99 2.42 2.08 2.42 2.29 2.01 (a) Show a dot plot of the data with both low and high temperature tensile strength values. (b) Compute sample mean tensile strength for both samples. (c) Does it appear as if curing temperature has an influence on tensile strength, based on the plot? Comment further. (d) Does anything else appear to be influenced by an increase in curing temperature? Explain.A certain polymer is used for evacuation systems for aircraft. It is important that the polymer be resistant to the aging process. Twenty specimens of the polymer were used in an experiment. Ten were assigned randomly to be exposed to an accelerated batch aging process that involved exposure to high temperatures for 10 days. Measurements of tensile strength of the specimens were made, and the following data were recorded on tensile strength in psi: No aging: 227 222 218 217 225 218 216 229 228 221 Aging: 219 214 215 211 209 218 203 204 201 205 (a) Do a dot plot of the data. (b) From your plot, does it appear as if the aging process has had an effect on the tensile strength of thispolymer? Explain. (c) Calculate the sample mean tensile strength of the two samples. (d) Calculate the median for both. Discuss the similarity or lack of similarity between the mean andmedian of each group.Delcon Properties is a commercial developer of shopping centers and malls in various places around the country. The company needs to analyze the eco- nomic feasibility of rainwater drains in a 60-acre area that it plans to develop. Since the development won't be started for 3 years, this large open space will be subject to damage from heavy thunder- storms that cause soil erosion and heavy rutting If no drains are installed, the cost of refilling and grading the washed out area is expected to be $1500 per thunderstorm. Alternatively, a temporary corrugated steel drainage pipe could be installed that will prevent the soil erosion. The cost of the pipe will be $3 per foot for the total length of 7000 feet required. Some of the pipe will be sal- vageable for $4000 at the end of the 3-year period between now and when the construction begins. Assuming that thunderstorms occur regularly at 3-month intervals, starting 3 months from now, which alternative should be selected on the basis of a present worth comparison using an interest rate of 4% per quarter?Construct a graph of the cumulative distribution function of Exercise 3. 15. Reference: Exercise 3. 15: Find the cumulative distribution function of the random variable X representing the number of defectives in Exercise 3.11. Then using F(x), find (a) P(X = 1); (b) P(0 ), for x = 0, 1, 2.The probability distribution of X, the number of imperfections per 10 meters of a synthetic fabric in continuous rolls of uniform width, is given by 1 2 3 I(x) 0.41 0.37 0.16 0.05 0.01 Construct the cumulative distribution function of X. Let X denote the diameter of an armored electric cable and Y denote the diameter of the ceramic mold that makes the cable. Both X and Y are scaled so that they range between 0 and 1. Suppose that X and Y have the joint density f (z, y) = - 01/2)